The authors have declared that no competing interests exist.
Conceived and designed the experiments: JM TS KD. Performed the experiments: JM. Analyzed the data: JM TS. Wrote the paper: JM KD.
The subcortical saccade-generating system consists of the retina, superior colliculus, cerebellum and brainstem motoneuron areas. The superior colliculus is the site of sensory-motor convergence within this basic visuomotor loop preserved throughout the vertebrates. While the system has been extensively studied, there are still several outstanding questions regarding how and where the saccade eye movement profile is generated and the contribution of respective parts within this system. Here we construct a spiking neuron model of the whole intermediate layer of the superior colliculus based on the latest anatomy and physiology data. The model consists of conductance-based spiking neurons with quasi-visual, burst, buildup, local inhibitory, and deep layer inhibitory neurons. The visual input is given from the superficial superior colliculus and the burst neurons send the output to the brainstem oculomotor nuclei. Gating input from the basal ganglia and an integral feedback from the reticular formation are also included.
We implement the model in the NEST simulator and show that the activity profile of bursting neurons can be reproduced by a combination of NMDA-type and cholinergic excitatory synaptic inputs and integrative inhibitory feedback. The model shows that the spreading neural activity observed in vivo can keep track of the collicular output over time and reset the system at the end of a saccade through activation of deep layer inhibitory neurons. We identify the model parameters according to neural recording data and show that the resulting model recreates the saccade size-velocity curves known as the saccadic main sequence in behavioral studies. The present model is consistent with theories that the superior colliculus takes a principal role in generating the temporal profiles of saccadic eye movements, rather than just specifying the end points of eye movements.
The mammalian visuomotor system is one of the best studied model systems for elucidating the computational principles of movement control and their neural implementation mechanisms. Within the visuomotor system, the superior colliculus (SC) plays a primary role in directing the gaze by eye and head movements by integrating multiple sensory and cognitive inputs
The aim of this study is to construct a realistic spiking neuron model of the SC that allows us to bring together the behavioral functions of eye movements, the anatomy and physiology of the SC circuit, and the biophysical properties of the SC neurons.
The SC is composed of the superficial, intermediate, and deep layers. The superficial SC receives visual input from the retina and from cortical visual areas
A major question about the function of the SC is whether it just specifies the location of a saccadic eye movement or is further involved in shaping of the dynamic pattern of eye movements
We first review the key anatomical and physiological features of the SC circuit and present the model structure (see
Each neuron model layer is spatially extended and organized in the same relative order as in the neural substrate. Feedback connections to the same node indicate layer intraconnections. Primary functional circuits are indicated by coloured connections. Red connections: Burst neuron burst profile circuit. Blue connections: Spreading inhibition and system reset. Grey shaded connections: inputs common to both circuits. See
The superficial SC consists of two interconnected layers and two major cell types – wide-field and narrow-field receptive cells – that project to the intermediate areas
Burst neurons send their output to the eye movement control nuclei in the brain stem. They act as regular spiking neurons when stimulated directly but exhibit bursting behaviour when they receive inputs from the superficial layer
Buildup neurons exhibit spreading activation during a saccade
In addition to local inhibitory inputs from within the intermediate SC, burst neurons also receive an extrinsic feedback loop from the saccade motor-related areas such as the central mesencephalic reticular formation (cMRF) that regulates the saccade magnitude and movement profile
Burst neurons in the rostral pole generate microsaccades during fixation in a manner similar to the saccade-generation circuitry in the caudal SC
There is considerable evidence for asymmetric large-scale spreading activation occurring in the intermediate SC during saccades in many animals
While the superior colliculus is implicated in the generation of saccades it is only one area in a large functional network that includes the Frontal Eye Fields and the Cerebellum. It is known that either SC or the FEF alone can generate saccades in the absence of the other in the primate
The horizontal and vertical eyeball motoneuron systems need to work in close synchrony in order to generate straight, on-target saccades. The movement initiation time and the movement profile over time both need to be closely coupled
If the superior colliculus indeed provides a movement profile for the brainstem eye-muscle driving neurons rather than just a target position, the burst cell output rate over time needs to follow a specific profile. Goossens and van Opstal
Curves show peak firing rate and peak-to-end firing time, where the end is taken when the curve drops below 1% of peak. Regenerated from
Goossens and van Opstal
The Cerebellum is heavily implicated in saccades downstream of the SC and FEF. The oculomotor vermis lesion causes significant dysmetria and large timing and end-goal variations, though saccades still exhibit distance-dependent variation of peak velocity and duration
Taken together it is plausible that the target selection and the movement profile is generated upstream of the cerebellum and motoneuron systems; that is, in the superior colliculus as well as in areas related to the FEF. SC burst neuron discharges encode a motor target as well as a time profile that drives brainstem eye-muscle driving neurons.
Our aim is to explore a possible neural circuit that can generate such a collicular burst neuron movement profile over time, subject to physiological and neurological constraints.
We are concerned in this paper with the direct subcortical saccade generation loop as an integrated sensory-motor system. We thus consider only the superior colliculus and leave the interaction with the frontal eye fields aside. This has some biological justification; so-called express saccades are visually triggered saccades with very short latency that are generated in a bottom-up fashion through the retina-SC-motor system loop without the involvement of cortical areas
Our model aims to replicate the SC of the macaque monkeys. However, when the anatomical of physiological data from macaques are not available, we use the data from other primates, rodents, or rabbits with appropriate scaling. In the following, the observations are from primates unless otherwise mentioned.
The overall structure of the SC model is illustrated in
Our proposed burst generation circuit consists of two mechanisms. The first is the activation of burst neurons by NMDA-type input from the QV neurons and the cholinergic input from the buildup neurons and the subsequent recurrent inhibition from the cMRF integrator neurons (
The spreading activation occurs among buildup neurons, while burst neuron activity remains confined to a restricted area around the stimulus origin. In order to recreate the experimentally observed rostral activity shift, we approximate the connection asymmetry with rostrally shifted wide-field Gaussian efferent projections and buildup neuron short-range interconnections (see
Connection | radius | sd | Wt | ConnP. |
Input |
1.5 | 0.6 |
|
0.07 |
Input |
0.2 | – |
|
0.25 |
wide |
0.2 | – |
|
0.25 |
wide |
0.2 | – | 0.25 | |
narrow |
0.2 | – |
|
0.25 |
narrow |
0.2 | – |
|
0.25 |
QV |
0.5 | 0.6 |
|
0.175 (1) |
QV |
0.6 | 0.4 |
|
0.25 |
InQV |
0.6 | 0.4 |
|
0.25 |
QV |
0.5 | 0.2 |
|
0.25 |
QV |
1.5 | 0.5 | (2) | 0.25 |
Build |
0.5 | 0.6 |
|
0.175 (1) |
Build |
0.5 | 0.4 |
|
0.25 |
Build |
0.6 | 0.4 |
|
0.25 |
InB |
0.6 | 0.4 |
|
0.25 |
Build |
2.0 | 1.0 |
|
0.05 |
Burst |
0.5 | 0.3 |
|
0.25 |
Burst |
0.5 | 0.1 |
|
0.025 |
Burst |
– | – | – | |
Inhib |
0.5 | 0.4 |
|
0.25 |
Inhib |
0.5 | 0.5 |
|
0.25 |
Inhib |
0.5 | 0.5 |
|
0.25 |
Inhib |
– | – |
|
– (3) |
INT |
– | – | (2) | – (3) |
INT |
– | – |
|
– (3) |
Radius: receptive radius, mm; sd: standard deviation, mm; Wt: weight (in terms of synaptic conductance); ConnP: interneuron connection probability.
input: input source; wide: Wide-field superficial neuron; narrow: Narrow field superficial neuron; QV: Quasivisual neuron; InQV: Quasivisual interneuron; Build: Buildup neuron; InB: Buildup interneuron; Burst: Burst neuron; Inhib: Deep layer inhibitory neuron; INT: cMRF integrator.
(1): interconnections are rostrally shifted by 0.3 mm, and with a 5 ms delay.
(2): Connection weight varies by a saccade angular distance-dependent factor; see Results for details.
(3): Integrator connections have 5 ms delay.
We propose that the amount of activation elicited by the spreading activation keeps track of overall system activity to act as a local shut-down mechanism. As activity increases through the buildup layer it eventually triggers deep layer inhibitory neurons in the deep SC
We first investigate the role of NMDA-type synapse in shaping the bursting neuron activity and find appropriate set of parameters to satisfy the constraint on the burst duration and spike counts. The responses to regular and to NMDA-type synaptic inputs are shown in
Input to a regular excitatory synapse (top) and to an NMDA-type synapse (bottom). A 50 pA input current is added between 50 ms and 100 ms. Model parameters in
In order to find the model parameters to satisfy the output spike patterns shown in
A Model peak-to-end burst time (orange contour plot) and equal peak burst rate (blue contour plot) as functions of QV
From the parametrized monkey data shown in
We need to satisfy the additional restriction that total spikes be constant for any angle saccade. In
We use this linear estimation to let the inhibitory and NMDA parameters vary as a function of radial angular distance in SC surface coordinates.
Here we report the overall dynamic operation of the network and show that the model can reproduce the major physiological features of the SC and saccadic eye movement. The time course of operation of the entire model is illustrated in
A, B: target input at 9
QV neurons and buildup neurons are activated by narrow- and wide-field neuron input in the superficial SC, and are reciprocally inhibited by their inhibitory interneurons (QV inhibitory interneurons not shown) (5D: −20 ms). When the burst neurons are released from SN inhibition at 0 ms, the burst neurons that receive both cholinergic input from the buildup neurons and NMDA input from the QV neurons will activate strongly (5B,D: 50 ms).
The burst output is projected to the spike integrator in the cMRF. This integrated output is projected back to the burst neurons where it inhibits the bursting activity, giving rise to the skewed burst activity profile. The integrator output also inhibits the inhibitory interneurons for the buildup neurons, where asymmetric intraconnections cause a controlled spread of activation over time. This spreading activation (5B: 120 ms, D: 125 ms) eventually triggers deep inhibitory neurons that in turn inhibits the burst and QV neurons (5B: 140 ms) and resets related areas to finish the saccade. The burst neuron activity causes eye movement with 20 ms latency
The saccade angle-dependent burst profiles is shown in
Shown for the same angles as in
The eye-movement profile – the saccade main sequence – is highly stereotypical and exhibits three distinctive features with the increase in the saccade angle: sub-linear increase in the peak eye movement speed, nearly linear increase in the saccade duration, and skewed velocity profiles with a nearly constant peak time. See
A: Peak saccade speed as a function of saccade distance. Circles are individual trials; solid line is the average per simulated distance; and dotted line is the hypothetical linear relation based on the 2
With a large-scale spiking-neuron level model we can make use of specific neurophysiological constraints as well as system-level and behavioural data. We can observe the activity of both individual model neurons and the resulting large-scale behaviour. That, in turn, enables us to compare model behaviour with experimental data at both large-scale and fine-grained levels.
We show that when taking small-scale neurophysiological structure and large-scale behaviour into account, our resulting model is consistent with theories, such as
Burst neurons driven by NMDA and cholinergic synaptic input exhibit sustained bursting, and an inhibitory feedback circuit between collicular burst neurons and a spike integrator circuit in the central mesencephalic reticular formation modulates the burst profile over time.
This study predicts that inhibition from the deep layer plays a role in stopping the eyes at the right time. This can be tested by selective manipulation of GABAergic neurons in the deep layer, which should be possible by using optogenetic methods. Moreover, the inhibitory neurons in the deep layer has been reported only in rabbits, so checking their existence in rodents and primates is also an important anatomical test.
The deep layer model neurons activate through mutual excitation; this mechanism is unrealistic but chosen for simplicity. NMDA receptor-based bursting or intrinsic bursting modulated through recurrent inhibition would be feasible mechanisms, but evidence for any mechanism is presently lacking.
A more specific prediction is that the balanced NMDA and inhibitory inputs as shown in
A straightforward relationship between saccade distance in collicular surface coordinates on one hand, and connection weights from buildup neurons and from a local spike integrator to burst neurons on the other, is sufficient to recreate the saccade target distance-related main sequence profile and peak skewness. With a theoretically derived distribution of weights from the SC to the motoneuron systems
Oblique saccades exhibit component-wise lower peak speed and longer duration than their purely horizontal or vertical counterparts
The superior colliculus is the final common point for the horizontal and vertical eye motoneuron systems in our model.
An open question concerns the functional significance of spreading activation seen in the intermediate superior colliculus. One suggestion is that the activity is tracking gaze direction error and that an end of saccade is triggered when the spreading activity reaches the collicular rostral pole
We suggest that spreading activation in the primate tracks saccade progression rather than gaze error; that total activation rather than the spatial spread is the significant measure; and that it terminates the saccade by activity level-induced deep neuron activation rather than rostral activation from the directional spread. In our view the spread is the means by which total buildup neuron activity increases over time.
We do not offer a functional explanation for the rostral shift in activity. The shift in primates is very weak for long saccades and might not have a significant functional role. In this work we have added a rostral shift to be in accord with the effect.
The connections between buildup and deep inhibitory neurons are uniform across the surface; the timing of the resulting saccade circuit termination is determined by the rate of spreading activation, which in turn is determined by the position-dependent interconnections in the burst neuron circuit. This termination not only prepares the system for a new saccade, but also directly improves the reliability of the burst generation circuit by regularizing the end of the burst envelope as seen in
Human peak saccade speed tapers off sharply after about 20
It is feasible to add rostral pole-mediated saccade inhibition and release to the model. Rostral fixation neurons poly-synaptically inhibit caudal SC burst neurons. Buildup neuron ramp-up would indirectly inhibit rostral fixation neurons that in turn releases the local inhibition and enable the release of the caudal saccade. The inhibition of burst and buildup neurons at the end of the saccade would in turn disinhibit rostral areas and re-enable caudal inhibition.
The present model lacks a true superficial division. We implement only the wide-field and narrow-field neurons that act as outputs to the intermediate areas, with no intraconnections; we also do not implement any input-specific intermediate circuits. Without a retinal model or a full superior division we had to simplify the visual input as a fixed, rather than transient, Poisson spike train, which we assume to be representative of the kind of input generated by the superficial division, the FEF and input-related intermediate circuits after regularization.
The model we have described here consists of only one superior colliculus. The lack of a interconnected pair implies that we can not correctly generate activity near the edges of the structure. The functional mapping between colliculi is fairly well understood
This spiking neuron-level model generates collicular burst neuron activity through NMDA synapse mediated bursting and an inhibitory feedback circuit, and presents a functional mechanism for the spreading activation in the SC that tracks collicular activity and terminates the saccade via deep layer inhibitory neuron activation. The current model is able to account for recorded burst neuron output profiles as seen in
We use the Adaptive Exponential Integrate and Fire (AEIaF) neuron model by Brette and Gerstner
Parameter | Value | Parameter | Value |
|
62/40 pF |
|
−47 mV |
|
4 nS |
|
−65 mV |
|
−65 mV |
|
2.0 mV |
|
|||
|
0.2 nS |
|
20 ms |
|
30 pA |
|
|
|
|||
|
0.0 mV |
|
−75.0 mV |
|
0.72 nS |
|
0.04 nS |
|
0.2 ms |
|
1.5 ms |
|
0.0 mV |
|
−51.8 mV |
|
1.2 nS |
|
1.367 |
|
3.0 ms |
Parameters used for the AEIaF neuron for the simulation model. Burst neurons have a membrane capacitance of 40 pF.
The membrane potential follows the differential equation
A spike event is triggered when the membrane potential diverges to infinity due to the exponential term; in practice a spike is triggered when
The synaptic conductances are shaped by an alpha function with the time
NMDA synapses are glutamatergic receptors sensitive to the membrane potential. We model an NMDA synapse as a sigmoidal function with center at
The synthetic cMRF integrator is implemented as a set of 100 integrator units whose firing rate in spikes/s is linearly proportional to the sum of weighted spikes received since reset:
The synaptic connectivity parameters are summarized in
Inputs are mapped to the superficial neurons with projections with a standard deviation of
The superficial neurons, QV, buildup and associated interneurons have a density of
Intraconnections in the model are Gaussian or flat (implemented by a wide Gaussian with cut-off):
Intraconnections in the intermediate model layers are all localized, less than
The weights from burst neurons to the horizontal and vertical motoneuron system is given by
We can obtain an estimate for the angular speed over time by determining the angular distance represented by each burst neuron spike.
The eye movement trajectory is estimated from the burst neuron output by accumulating the small eye displacement encoded by each spike, which is given by the horizontal and vertical angles (9) and (10) divided by the average total spikes (1485) for a saccade.
Collicular output is gain-adapted downstream of the burst neuron output
To guide our model parameter estimation we assume that a saccade burst is over when the rate drops below 1% of the peak value. Due to the stochastic nature of our model we estimate the burst end in the simulations to be when activity drops below 10% of the peak rate.
We are very grateful to the Riken Integrated Cluster of Clusters (RICC) at RIKEN for supplying the computing resources, and to the Next Generation Supercomputing Project and MEXT (Ministry of of Education, Culture, Sports, Science, and Technology) in Japan for the support. We also thank Drs. Yasushi Kobayashi, Tadashi Ogawa and Kae Nakamura for very productive discussions.